In character mode, there doesn't seem to be a direct way of pasting the clipboard into the terminal (i.e. send it).
Yes, you can use the command line or the editor, but I like the way (or, at least, I am used to the way) in PuTTY you can just right-click on the screen and it will paste.
Ctrl-V doesn't appear to do anything, although it is actually sending <22> so I assume that's correct.
Edit, Paste does nothing at all.
Right-click on the screen does not produce any Paste option.

Note that the current ways of pasting are not ideal, because sometimes you want to paste without a carriage return.

Paste doesn't really make sense when not in character mode. In character mode, Paste will paste the clipboard to the server. When not in character mode, the screen is "read-only" so there is no way to paste into it. You can right-click on the command line and select Paste if that is what you want.